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energies Article A Fuzzy-Based PI Controller for Power Management of a Grid-Connected PV-SOFC Hybrid System Shivashankar Sukumar 1, * ID , Marayati Marsadek 1 , Agileswari Ramasamy 2 , Hazlie Mokhlis 3 and Saad Mekhilef 4 1 Institute of Power Engineering (IPE), Universit Tenaga Nasional, Selangor 43000, Malaysia; [email protected] 2 Department of Electronics and Communication Engineering, Universiti Tenaga Nasional, Selangor 43000, Malaysia; [email protected] 3 Department of Electrical Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia; [email protected] 4 Power Electronics and Renewable Energy Research Laboratory (PEARL), University of Malaya, Kuala Lumpur 50603, Malaysia; [email protected] * Correspondence: [email protected]; Tel.: +60-11-53563676 Academic Editor: William Holderbaum Received: 11 September 2017; Accepted: 16 October 2017; Published: 27 October 2017 Abstract: Solar power generation is intermittent in nature. It is nearly impossible for a photovoltaic (PV) system to supply power continuously and consistently to a varying load. Operating a controllable source like a fuel cell in parallel with PV can be a solution to supply power to variable loads. In order to coordinate the power supply from fuel cells and PVs, a power management system needs to be designed for the microgrid system. This paper presents a power management system for a grid-connected PV and solid oxide fuel cell (SOFC), considering variation in the load and solar radiation. The objective of the proposed system is to minimize the power drawn from the grid and operate the SOFC within a specific power range. Since the PV is operated at the maximum power point, the power management involves the control of SOFC active power where a proportional and integral (PI) controller is used. The control parameters of the PI controller K p (proportional constant) and T i (integral time constant) are determined by the genetic algorithm (GA) and simplex method. In addition, a fuzzy logic controller is also developed to generate appropriate control parameters for the PI controller. The performance of the controllers is evaluated by minimizing the integral of time multiplied by absolute error (ITAE) criterion. Simulation results showed that the fuzzy-based PI controller outperforms the PI controller tuned by the GA and simplex method in managing the power from the hybrid source effectively under variations of load and solar radiation. Keywords: distributed generation; fuel cell; fuzzy logic controller; hybrid system; power management; photovoltaic 1. Introduction Renewable energy sources such as wind turbines and photovoltaics (PV) have gained prominence in generating electricity due to environmental concerns. A reduction in CO 2 emission and the combustion of fossil fuels are among the main benefits of using these sources. At the end of 2014, renewable energy sources contributed to 22.8% of global electricity production [1]. During the period of 2009–2014, the annual growth rate of solar PV capacity was higher among other renewable energy sources. Solar PV can supply a local load that is referred to as a microgrid system. The microgrid can operate in parallel with the grid or in islanded mode. In grid-connected mode, depending on both the generation and load demand, the microgrid absorbs or supplies power from/to the grid. The main challenge Energies 2017, 10, 1720; doi:10.3390/en10111720 www.mdpi.com/journal/energies

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Page 1: A Fuzzy-Based PI Controller for Power Management of a Grid ...eprints.um.edu.my/19017/1/A_fuzzy-based_PI... · control static synchronous compensator (STATCOM) installed in a power

energies

Article

A Fuzzy-Based PI Controller for Power Managementof a Grid-Connected PV-SOFC Hybrid System

Shivashankar Sukumar 1,* ID , Marayati Marsadek 1, Agileswari Ramasamy 2, Hazlie Mokhlis 3

and Saad Mekhilef 4

1 Institute of Power Engineering (IPE), Universit Tenaga Nasional, Selangor 43000, Malaysia;[email protected]

2 Department of Electronics and Communication Engineering, Universiti Tenaga Nasional,Selangor 43000, Malaysia; [email protected]

3 Department of Electrical Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia;[email protected]

4 Power Electronics and Renewable Energy Research Laboratory (PEARL), University of Malaya,Kuala Lumpur 50603, Malaysia; [email protected]

* Correspondence: [email protected]; Tel.: +60-11-53563676

Academic Editor: William HolderbaumReceived: 11 September 2017; Accepted: 16 October 2017; Published: 27 October 2017

Abstract: Solar power generation is intermittent in nature. It is nearly impossible for a photovoltaic(PV) system to supply power continuously and consistently to a varying load. Operating a controllablesource like a fuel cell in parallel with PV can be a solution to supply power to variable loads.In order to coordinate the power supply from fuel cells and PVs, a power management systemneeds to be designed for the microgrid system. This paper presents a power management systemfor a grid-connected PV and solid oxide fuel cell (SOFC), considering variation in the load and solarradiation. The objective of the proposed system is to minimize the power drawn from the grid andoperate the SOFC within a specific power range. Since the PV is operated at the maximum powerpoint, the power management involves the control of SOFC active power where a proportional andintegral (PI) controller is used. The control parameters of the PI controller Kp (proportional constant)and Ti (integral time constant) are determined by the genetic algorithm (GA) and simplex method.In addition, a fuzzy logic controller is also developed to generate appropriate control parametersfor the PI controller. The performance of the controllers is evaluated by minimizing the integral oftime multiplied by absolute error (ITAE) criterion. Simulation results showed that the fuzzy-based PIcontroller outperforms the PI controller tuned by the GA and simplex method in managing the powerfrom the hybrid source effectively under variations of load and solar radiation.

Keywords: distributed generation; fuel cell; fuzzy logic controller; hybrid system; power management;photovoltaic

1. Introduction

Renewable energy sources such as wind turbines and photovoltaics (PV) have gained prominence ingenerating electricity due to environmental concerns. A reduction in CO2 emission and the combustionof fossil fuels are among the main benefits of using these sources. At the end of 2014, renewable energysources contributed to 22.8% of global electricity production [1]. During the period of 2009–2014,the annual growth rate of solar PV capacity was higher among other renewable energy sources.Solar PV can supply a local load that is referred to as a microgrid system. The microgrid can operate inparallel with the grid or in islanded mode. In grid-connected mode, depending on both the generationand load demand, the microgrid absorbs or supplies power from/to the grid. The main challenge

Energies 2017, 10, 1720; doi:10.3390/en10111720 www.mdpi.com/journal/energies

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Energies 2017, 10, 1720 2 of 17

of using PV is its dependence on the solar radiation level. Thus, it is nearly impossible to satisfya variable load since the output power from the PV varies. In order to overcome this shortcoming,a controllable source such as a fuel cell can be installed and operate in parallel with the PV. Fuel cells arechosen because of their (i) high energy conversion; (ii) zero emission of pollutant gases; (iii) noiselessoperation; and (iv) high reliability. Among other fuel cell technologies, the solid oxide fuel cell (SOFC)is an attractive option for distributed generation applications. Practical application of SOFC in powerproduction is reported in [2]. In this paper, a 100 kW SOFC unit was installed and operated for morethan 15,000 h at a power plant in Westervoort, Netherlands, proving the point that SOFC is reliableenough for commercial power generation.

A microgrid system consisting of PV and SOFC can operate in grid-connected or islanded mode.During grid-connected operation, the system should be managed well in order to coordinate powergeneration between PV and SOFC, and at the same time ensure that load demand is fulfilled. In thiscontext, an efficient power management system is required. If the total power from the hybrid systemis less than the load demand, the microgrid imports power from the grid. If the power produced fromthe hybrid source is more than the load demand, the excess power is injected into the grid. SinceSOFC is a controllable source, its output power should be regulated to its reference value specifiedby the power management system. The microgrid power management system assigns a reference setpoint for the generation units. Therefore, the generation unit should have appropriate control schemesfor their voltage source inverter (VSI) in order to position its output power to the reference pointsassigned by power management systems. It is necessary for a control scheme to attain fast responseand maintain system stability during sudden changes.

In [3] a power management strategy is developed for a hybrid system consisting of PV anda proton exchange membrane fuel cell (PEMFC) supplying power to a variable load. The authorsdeveloped a detailed model of PV, PEMFC and electrolyser. The authors used an artificial neuralnetwork (ANN) for maximum power point tracking (MPPT). They claimed that the ANN for MPPTproduced the best results for real weather conditions. Here the PEMFC is seen as a secondarygenerator which works when PV power is absent. This paper deals only with the management ofthe hybrid system, which operates in an islanded mode. Similar work was carried out in [4], wheretwo intermittent sources (PV and wind) along with a fuel cell were used to deliver DC load. Theyemployed fuzzy logic control to achieve maximum power tracking for wind and PV. The hybrid systemwas operating in islanded mode. In [5], a power management strategy for a grid-connected PV-FChybrid source was presented where the hybrid sources were operating in unit power control and feederflow control modes. The strategy is to operate PV at MPPT and the fuel cell within its power range andreduce the number of switches between the two control modes. In [3,6] a power management systemis proposed for a hybrid system consisting of PV-FC operated in islanded mode. However, the authorsdid not mention the controller used or the selection of parameters for the controller. In [7], a differentialevolution algorithm was used to find the optimal control parameters for a PI controller. The robustnessof the controller was evaluated only for the SOFC system operating in parallel with the grid. A fuzzylogic controller for tuning the PI controller parameters was designed in [8] specifically for inverterreactive power control. In [9] a PI tuning method is proposed for the energy management of a DCmicrogrid grid. The tuning of the PI controller used a swarm variant of hybrid mean variance mappingoptimization. Although they used optimization to tune the controller’s parameters, it may be difficultto implement this in real time. An optimal controller was presented in [10] for a grid-connectedmicrogrid operation considering changes in the load. In this work, the control parameters weretuned using the particle swarm optimization (PSO) technique. The operating range of the distributedsource, a constraint, was not considered, and the robustness of the controller was demonstrated fora single step change in the load. In addition, the reference set point which was given as an inputto distributed generator’s (DG) control was fixed. From the above references, it can be confirmedthat many researchers focused on the design of power management for the operation of hybridsystems. However, there is very limited research that focuses on the selection of control parameters

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Energies 2017, 10, 1720 3 of 17

for the distributed generator’s (DG) real power controllers. Moreover, most of it only considers caseswhere DG output is constant. Hence, there is a need to look into this matter, which will be addressedin this paper.

Fuzzy logic is mathematical tool which provides solutions for a complex problem where thereis no well-defined mathematical formulation. Mamdani and Takagi Sugeno interface fuzzy systemsare commonly used for control applications. An application of a mamdani interface system is foundin [11] where a fuzzy-based speed governor was designed for a mini hydro power plant that suppliesvarying load. In [12] an adaptive fuzzy logic controller was designed using a mamdani interfacesystem for load frequency control of a small hydro plant. Some applications of Takagi Sugeno fuzzysystems are presented in [13,14]. In [13], a Takagi Sugeno fuzzy system is designed to efficientlycontrol static synchronous compensator (STATCOM) installed in a power system network undervarious disturbances. The voltage and frequency of an isolated wind turbine controlled by a TakagiSugeno fuzzy logic controller considering variation in wind speed and load power can be foundin [14]. A fuzzy logic system integrated with an optimization technique to provide fast and robustresults has been presented in [15–18]. In [15], a fuzzy-logic–genetic-algorithm model is developed toestimate monthly solar radiation. The results presented in [15] indicate that the fuzzy–genetic modelmore accurately estimates the monthly solar radiation than an artificial neural network (ANN) andneuro fuzzy model. The application of a fuzzy-based controller to tune the PI control parameters fora hybrid electric vehicle application is found in [16]. A cuckoo-search-optimization-based fuzzy logiccontroller is developed in [17] to operate a hybrid system consisting of PV, battery and diesel generatorin standalone mode. PSO used to tune the membership function of a fuzzy controller for solar PVMPPT control is carried out in [18]. Application of fuzzy logic to solve diverse engineering problemscan be found in the literature; however, the application of fuzzy to find the PI controller parameters fora DG used in a power management problem is very limited.

In this paper, a power management algorithm is developed for a grid-connected PV-SOFC hybridsystem, taking into consideration variation in the load and solar radiation. When the system is inoperation, the power management system facilitates PV to operate at the maximum power point,minimizing the power drawn from the grid and operating the fuel cell within its operating efficiency.The control of the power from the hybrid source is possible by controlling the power output fromthe SOFC system. Here, a PI controller is employed to control the active power flow from the SOFCsystem. A fuzzy logic system, genetic algorithm and simplex are designed to obtain the optimalcontrol parameters (Kp and Ti) for the PI controller, taking into consideration variation in the load andsolar radiation. The integral of time multiplied by absolute error (ITAE) criterion is used to evaluatethe performance of the controllers. The SOFC operates within a specific power range (PFCmin,PFCmax). The simulation model of the grid-connected PV-SOFC was built in PSCAD software.

2. System Description

The proposed microgrid incorporates two electronically-interfaced distributed generators (DG)connected through a three-phase voltage source converter (VSC). A 100 kW SOFC is the primarypower source. Since minimizing the power drawn from the grid is considered as one of the objectives,the SOFC is sized to the peak load where the fuel cell is able to supply power to the variable load inthe absence of PV. The load demand varies throughout 24 h. A 200 kW PV is also connected wherethe available power is injected into the microgrid system with a unity power factor. The microgridoperates in grid-connected mode.

2.1. Hybrid Grid-Connected PV-SOFC System

The microgrid system considered here consists of a 200 kW PV array and 100 kW SOFC connected tothe point of common coupling through a 0.4/11 kV transformer (Figure 1). The system is grid-connectedand operates in parallel with variable load.

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Energies 2017, 10, 1720 4 of 17Energies 2017, 10, 1720    4 of 17 

 

Figure 1. Grid‐connected hybrid system. 

2.2. PV Array Model 

An electrical equivalent of solar cell is modeled by connecting a current source anti‐parallel with 

a diode which is shown in Figure 2 [19].   

 

Figure 2. Equivalent circuit of single diode solar cell. 

When  solar  radiation  falls  on  a  solar  cell,  a  DC  photo  current  (Ip)  is  generated.  Ip  varies 

proportionally with changes in solar radiation. Applying Kirchhoff’s current law to the equivalent 

circuit gives [20],   

shdp IIII   (1) 

The diode current (Id) can be calculated as, 

sh

s

c

sod R

IRV

qnkT

IRVII ]1

/[exp   (2) 

Io is the dark current and can be calculated as, 

nk

qe

TTT

TII g

ccrefcref

corefo

11exp3

3

  (3) 

where, 

Ioref: dark current at Tcref; 

k: Boltzman constant; 

eg: band gap energy; 

Tcref: reference cell temperature; 

Tc: cell temperature; 

Figure 1. Grid-connected hybrid system.

2.2. PV Array Model

An electrical equivalent of solar cell is modeled by connecting a current source anti-parallel witha diode which is shown in Figure 2 [19].

Energies 2017, 10, 1720    4 of 17 

 

Figure 1. Grid‐connected hybrid system. 

2.2. PV Array Model 

An electrical equivalent of solar cell is modeled by connecting a current source anti‐parallel with 

a diode which is shown in Figure 2 [19].   

 

Figure 2. Equivalent circuit of single diode solar cell. 

When  solar  radiation  falls  on  a  solar  cell,  a  DC  photo  current  (Ip)  is  generated.  Ip  varies 

proportionally with changes in solar radiation. Applying Kirchhoff’s current law to the equivalent 

circuit gives [20],   

shdp IIII   (1) 

The diode current (Id) can be calculated as, 

sh

s

c

sod R

IRV

qnkT

IRVII ]1

/[exp   (2) 

Io is the dark current and can be calculated as, 

nk

qe

TTT

TII g

ccrefcref

corefo

11exp3

3

  (3) 

where, 

Ioref: dark current at Tcref; 

k: Boltzman constant; 

eg: band gap energy; 

Tcref: reference cell temperature; 

Tc: cell temperature; 

Figure 2. Equivalent circuit of single diode solar cell.

When solar radiation falls on a solar cell, a DC photo current (Ip) is generated. Ip variesproportionally with changes in solar radiation. Applying Kirchhoff’s current law to the equivalentcircuit gives [20],

I = Ip − Id − Ish (1)

The diode current (Id) can be calculated as,

Id = Io[exp(

V+IRsnkTc/q

)− 1]−

(V+IRs

Rsh

)(2)

Io is the dark current and can be calculated as,

Io = Iore f

(Tc

3

Tcre f3

)exp[(

1Tcre f− 1

Tc

)]qegnk (3)

where,

Ioref: dark current at Tcref;

k: Boltzman constant;eg: band gap energy;Tcref: reference cell temperature;

Tc: cell temperature;q: electron charge;

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Energies 2017, 10, 1720 5 of 17

n: diode ideality factor.

Ip depends on solar radiation and temperature and can be expressed as,

Ip = ISCre fG

Gre f

[1 + αt

(Tc − Tcre f

)](4)

where,

Gref: reference solar radiation;

αt: temperature coefficient of photo current.

PV cells are connected in series/parallel combination to make the PV module. The PV modulesare arranged in series and in parallel combination to generate the required electrical power. A 200 kWPV plant is built by connecting 40 strings in parallel where each string contains 20 modules in a series.The electrical specifications of the PV module is obtained from [21].

The MPPT controller connected to the DC/DC converter of PV always captures the maximumpower from a solar cell. MPPT algorithms such as incremental conductance (IC), perturbation andobservation (P&O), and constant voltage are the common techniques found in the literature. Amongthese techniques, the IC algorithm is the simplest and most effective technique that is used widely.The IC algorithm is the fastest in MPPT under rapid weather changing conditions and the poweroscillation is negligible at the maximum power point [22]. For this reason, the IC algorithm method isused in this work.

2.3. SOFC Model

The SOFC is a distributed generator (DG) technology that generates power from chemicalreactions. The advantages of using SOFC over other fuel cells are long term stability and fuel flexibility;the electrical efficiency of a typical SOFC power plant can reach up to 70% [23]. A grid-connected SOFCdeveloped using PSCAD software is presented in [24]. The output fuel cell stack voltage consideringohmic loss is given by [25],

V = No[

Eo + RT2F

(ln

pH2 p0.5O2

pH2O

)]− rI f c (5)

where,

Ifc: fuel cell current;

R: universal gas constant;T: absolute temperature in kelvin;PH2 , PO2 and PH2O: partial pressure of hydrogen, oxygen and water;r: representation of ohmic loss in ohm;F: Faraday’s constant;Eo: ideal standard potential;No: number of cells in series in the stack.

The utilization factor and temperature of the stack are critical operating variables of SOFC.The utilization factor is the ratio between fuel consumed to total fuel input and the range of the utilizationfactor should be 80–90% [26]. For this work, the utilization factor is taken as a constant value of 85%and the operating temperature is kept constant at 1273 K [26]. The parameters of the 100 kW SOFCpower plant are obtained from [27].

3. Proposed Operating Strategy of Hybrid System

The hybrid system supplies power at a variable load throughout the day. The power managementsystem coordinates DG output (in this case PV and SOFC) in order to supply the variable load. In this

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Energies 2017, 10, 1720 6 of 17

operating strategy, the power from SOFC is regulated to its reference value. To coordinate the PV-SOFCoperation, an appropriate reference value must be set to the operating constraints of the DGs. Oncethe SOFC operating limit is known, the operating strategy depends on load variation and PV outputpower. When hybrid power supplies the load in grid-connected mode, the power balance equation isgiven by,

PPV + PFC + PGRID = PLOAD (6)

Since the power drawn from the grid (PGRID) incurs costs, the PGRID has to be minimized.Therefore the value of PGRID is set to zero.

PPV + PFC = PLOAD (7)

The operating limit of SOFC output power is given as follows,

PHYre f = PPV + PFCre f (8)

In Equation (7), when PV output (PPV) varies, the balance power is compensated by SOFC (PFC).The fuel cell supplies power based on its reference value (PFCref). Therefore, the total power fromthe hybrid generators is regulated to its reference value (PHYref). The reference of the hybrid system isgiven by,

PHYre f = PPV + PFCre f (9)

Figure 3 shows the operating strategy of a fuel cell when PPV equals zero. The references for fuelcell and hybrid system generation are given in Equations (10) and (11), respectively.

PiFCre f = Pi

Load, i = 0, 1, 2, 3, . . . n (10)

PiHYre f = P0

PV + PiFCre f , i = 0, 1, 2, 3, . . . n (11)

In the absence of PPV generation, only the fuel cell has to supply power to the varying load. Forexample, when load demand increases from PLoad 1 to PLoad 2, the change in the load is assigned asthe fuel cell reference set point (PFCref 2). Therefore, the SOFC delivers the required power (PFC 2)following the reference set point. Since the PV is absent, the total power generated from the hybridsource is equal to PFCref 2. In this way, if the load demand reaches the maximum value PLoad n, which is100 kW, fuel cell generation is also increased to its maximum capacity PFCmax following its referencePFCref n. For load increment or decrement, the change in PFCref and PHYref is shown in Figure 3. It shouldbe noted that PLoad 0 is the load demand equal to or less than 20 kW. Here, the power from the SOFC isfixed at PFCmin i.e., 20 kW.

When PPV is greater than zero, the operating strategy depends on PV output power and loadvariation. PV power and load variation are time dependent. In the case when PV power is available butless than the load, the SOFC supplies the deficit in power and the power from the grid is maintained atzero in order to reduce the cost for the power drawn from the utility grid. Therefore the target hybridreference power is given as,

PHYre f (t) = PPV(t) + PFCre f (t) + PGrid(t) (12)

where,PFCre f (t) = PLoad(t)− PPV(t), PGrid(t) = 0 (13)

In the case where PV power is more than the load, the excess power is injected into the grid wherethe value will be negative. In this case the fuel cell power PFCref is fixed to a minimum operating point(PFCmin), that is, 20 kW in order to avoid the underused condition, as this will lead to unexpected highcell voltages. Then the target reference power is given as,

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Energies 2017, 10, 1720 7 of 17

PHYre f (t) = PPV(t) + PFCre f (t) + PGrid(t) (14)

where,PFCre f (t) = 20 kW, PGrid(t) = PLoad(t)− PPV(t) (15)

It should be noted that the PFC is operated taking into consideration the constraint as stated inEquation (8). The complete control algorithm for the power management module is shown in Figure 4.

Energies 2017, 10, 1720    6 of 17 

variable load. In this operating strategy, the power from SOFC is regulated to its reference value. To 

coordinate  the PV‐SOFC  operation,  an  appropriate  reference  value must  be  set  to  the  operating 

constraints of the DGs. Once the SOFC operating limit is known, the operating strategy depends on 

load variation and PV output power. When hybrid power supplies the load in grid‐connected mode, 

the power balance equation is given by, 

LOADGRIDFCPV PPPP   (6) 

Since the power drawn from the grid (PGRID) incurs costs, the PGRID has to be minimized. Therefore 

the value of PGRID is set to zero. 

LOADFCPV PPP   (7) 

The operating limit of SOFC output power is given as follows, 

FCrefPVHYref PPP   (8) 

In Equation (7), when PV output (PPV) varies, the balance power is compensated by SOFC (PFC). 

The fuel cell supplies power based on its reference value (PFCref). Therefore, the total power from the 

hybrid generators  is regulated  to  its reference value  (PHYref). The reference of  the hybrid system  is 

given by, 

FCrefPVHYref PPP   (9) 

Figure 3 shows the operating strategy of a fuel cell when PPV equals zero. The references for fuel 

cell and hybrid system generation are given in Equations (10) and (11), respectively.   

… 3, 2, 1, 0,= , niPP iLoad

iFCref   (10) 

… 3, 2, 1, 0,= ,0 niPPP iFCrefPV

iHYref   (11) 

In the absence of PPV generation, only the fuel cell has to supply power to the varying load. For 

example, when load demand increases from PLoad 1 to PLoad 2, the change in the load is assigned as the 

fuel cell reference set point (PFCref 2). Therefore, the SOFC delivers the required power (PFC 2) following 

the reference set point. Since the PV is absent, the total power generated from the hybrid source is 

equal to PFCref 2. In this way, if the load demand reaches the maximum value PLoad n, which is 100 kW, 

fuel cell generation is also increased to its maximum capacity PFCmax following its reference PFCref n. For 

load increment or decrement, the change in PFCref and PHYref is shown in Figure 3. It should be noted 

that PLoad 0 is the load demand equal to or less than 20 kW. Here, the power from the SOFC is fixed at 

PFCmin i.e., 20 kW.   

 

Figure 3. Operating strategy of fuel cell when PPV0 = 0. Figure 3. Operating strategy of fuel cell when PPV0 = 0.

Energies 2017, 10, 1720    7 of 17 

When PPV is greater than zero, the operating strategy depends on PV output power and  load 

variation. PV power and load variation are time dependent. In the case when PV power is available 

but  less  than  the  load,  the  SOFC  supplies  the  deficit  in  power  and  the  power  from  the  grid  is 

maintained at zero in order to reduce the cost for the power drawn from the utility grid. Therefore 

the target hybrid reference power is given as, 

)()()()( tPtPtPtP GridFCrefPVHYref   (12) 

where, 

)()()( tPtPtP PVLoadFCref ,  0)( tPGrid   (13) 

In the case where PV power  is more than the  load, the excess power  is  injected  into the grid 

where the value will be negative. In this case the fuel cell power PFCref is fixed to a minimum operating 

point (PFCmin), that is, 20 kW in order to avoid the underused condition, as this will lead to unexpected 

high cell voltages. Then the target reference power is given as, 

)()()()( tPtPtPtP GridFCrefPVHYref   (14) 

where, 

kW20)( tPFCref ,  )()()( tPtPtP PVLoadGrid   (15) 

It should be noted that the PFC is operated taking into consideration the constraint as stated in 

Equation (8). The complete control algorithm for the power management module is shown in Figure 

4. 

 

Figure 4. Control algorithm for power management system. 

 

Figure 4. Control algorithm for power management system.

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Energies 2017, 10, 1720 8 of 17

4. Methodology

4.1. Control of SOFC Voltage Source Inverter (VSI)

The voltage and active power flow from the inverter output is regulated by adjusting the modulationindex and phase angle of the inverter, respectively. Regulating the inverter terminal voltage determinesthe reactive power flow as well. During the operating strategy, the fuel cell reference value can beachieved by controlling fuel cell power to the desired level. The PI controller is employed for betterdynamic response. In this paper, PI controllers are utilized to generate the modulation index andphase angle. From Figure 5, the active power from the fuel cell output is controlled by controlling itsdirect sequence component. From the meter installed at the inverter output, the actual output power iscalculated and is compared with its reference, which is produced from the power management system.The error signal of the active power is given as the input to the PI controller. The controller generatesa reference direct axis component from the error signal and is fed into dq0 to abc transformationblock. Finally the control signals for the inverter are generated by the pulse width modulation(PWM) technique.

This work focuses on implementing fuzzy logic to generate appropriate control values for a realpower controller where the real power error signal is given as an input to the MATLAB-fuzzy interfacesystem (FIS) system. The FIS system in turn generates the appropriate proportional gain (Kp) andintegral time constant (Ti) which are then used as input for the PI controller. Here, the SOFC referenceset point (PFCref) is generated from the power management system module.

Energies 2017, 10, 1720    8 of 17 

4. Methodology 

4.1. Control of SOFC Voltage Source Inverter (VSI) 

The  voltage  and  active  power  flow  from  the  inverter  output  is  regulated  by  adjusting  the 

modulation  index and phase angle of  the  inverter,  respectively. Regulating  the  inverter  terminal 

voltage determines  the  reactive power  flow  as well. During  the  operating  strategy,  the  fuel  cell 

reference value can be achieved by controlling fuel cell power to the desired level. The PI controller 

is employed  for better dynamic response.  In  this paper, PI controllers are utilized  to generate  the 

modulation  index and phase angle. From Figure 5,  the active power  from  the  fuel  cell output  is 

controlled by  controlling  its direct  sequence  component. From  the meter  installed at  the  inverter 

output, the actual output power is calculated and is compared with its reference, which is produced 

from the power management system. The error signal of the active power is given as the input to the 

PI controller. The controller generates a reference direct axis component from the error signal and is 

fed into dq0 to abc transformation block. Finally the control signals for the inverter are generated by 

the pulse width modulation (PWM) technique. 

This work focuses on implementing fuzzy logic to generate appropriate control values for a real 

power  controller where  the  real  power  error  signal  is  given  as  an  input  to  the MATLAB‐fuzzy 

interface system (FIS) system. The FIS system in turn generates the appropriate proportional gain (Kp) 

and  integral time constant (Ti) which are then used as  input for the PI controller. Here, the SOFC 

reference set point (PFCref) is generated from the power management system module. 

 

Figure 5. Solid oxide fuel cell (SOFC) active power control. 

The PI controller used in the SOFC active power control should be robust in nature when the 

system  is  operating  under  dynamic  changes  such  as  PV  output  and  load.  Therefore,  optimal 

operation of the PI controller is necessary. The optimal values for the real power controller Kp and Ti 

is determined using a fuzzy logic controller. For comparison, the GA and simplex method were also 

used to determine the control parameters of the PI controller. In this work, the controller’s objective 

function is to minimize the error using the ITAE performance criterion. The advantage of using the 

ITAE  performance  criterion  is  that  it  produces  smaller  overshoot  and  oscillations  [28].  The 

mathematical expression for the ITAE criterion is given as: 

dttetJ ).)(.(0

  (16) 

where, 

t is the time; 

Figure 5. Solid oxide fuel cell (SOFC) active power control.

The PI controller used in the SOFC active power control should be robust in nature whenthe system is operating under dynamic changes such as PV output and load. Therefore, optimaloperation of the PI controller is necessary. The optimal values for the real power controller Kp and Ti isdetermined using a fuzzy logic controller. For comparison, the GA and simplex method were also usedto determine the control parameters of the PI controller. In this work, the controller’s objective functionis to minimize the error using the ITAE performance criterion. The advantage of using the ITAEperformance criterion is that it produces smaller overshoot and oscillations [28]. The mathematicalexpression for the ITAE criterion is given as:

J =∞∫0(t.|e(t)|).dt (16)

where,

t: time;

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Energies 2017, 10, 1720 9 of 17

e(t): the difference between reference power and the actual fuel cell power.

To increase the robustness of the controller, the optimization is performed on all hourly datafor the entire day, which means that the ITAE index is optimized for 24 different operating points.Therefore, Equation (14) is rewritten for 24 different operating points. The objective function is given as,

J =24∑

n=0

∞∫0(t.|e(t)|).dt, n = 0, 1, 2, . . . 24 (17)

4.2. Proposed Fuzzy-Based PI Controller Model

The fuzzy-based PI controller was modeled in the PSCAD environment using the SOFC-fuzzyinterface system (FIS). Figure 6 shows a block diagram of the fuzzy-logic-based PI control. A FORTRANsubroutine was written in PSCAD to interface with the MATLAB engine.

Energies 2017, 10, 1720    9 of 17 

e(t) is the difference between reference power and the actual fuel cell power. 

To increase the robustness of the controller, the optimization is performed on all hourly data for 

the  entire day, which means  that  the  ITAE  index  is optimized  for  24 different operating points. 

Therefore, Equation (14) is rewritten for 24 different operating points. The objective function is given 

as, 

24 ... 2, 1, 0, = ,|).)(|.(24

0 0

ndttetJn

  (17) 

4.2. Proposed Fuzzy‐Based PI Controller Model 

The fuzzy‐based PI controller was modeled in the PSCAD environment using the SOFC‐fuzzy 

interface  system  (FIS).  Figure  6  shows  a  block  diagram  of  the  fuzzy‐logic‐based  PI  control.  A 

FORTRAN subroutine was written in PSCAD to interface with the MATLAB engine.   

 

Figure 6. Block diagram for fuzzy‐based proportional and integral (PI) control. 

The MATLAB‐FIS  system has one  input  (PFCref) and  two outputs  (Kp and Ti). The FIS  system 

receives PFCref as the input signal, and depending on the input signal an appropriate control parameter 

is sent back to the SOFC active power controller in the PSCAD environment. The FIS system consists 

of three important steps: (i) fuzzification; (ii) rule base mechanism; and (iii) defuzzification. As a first 

step,  a  set  of  input  data  (PFCref)  are  converted  into  a  fuzzy  set  using  a membership  function. A 

membership function is used in the fuzzification and defuzzification process where the set of non‐

fuzzy  inputs  is  mapped  to  fuzzy  sets.  For  this  work,  a  triangular  membership  function  was 

constructed for PFCref, Kp and Ti, given in Figure 7. The linguistic variables of input PFCref are denoted 

as Ref 1 to Ref 8, shown in Figure 7a. The linguistic variables of the output are indicated as Kp1 to Kp5 

for Kp in Figure 7b and Ti1 to Ti5 for Ti in Figure 7c, respectively. 

(a)

 (b)

Figure 6. Block diagram for fuzzy-based proportional and integral (PI) control.

The MATLAB-FIS system has one input (PFCref) and two outputs (Kp and Ti). The FIS systemreceives PFCref as the input signal, and depending on the input signal an appropriate control parameteris sent back to the SOFC active power controller in the PSCAD environment. The FIS system consists ofthree important steps: (i) fuzzification; (ii) rule base mechanism; and (iii) defuzzification. As a first step,a set of input data (PFCref) are converted into a fuzzy set using a membership function. A membershipfunction is used in the fuzzification and defuzzification process where the set of non-fuzzy inputs ismapped to fuzzy sets. For this work, a triangular membership function was constructed for PFCref, Kp

and Ti, given in Figure 7. The linguistic variables of input PFCref are denoted as Ref 1 to Ref 8, shownin Figure 7a. The linguistic variables of the output are indicated as Kp1 to Kp5 for Kp in Figure 7b andTi1 to Ti5 for Ti in Figure 7c, respectively.

Energies 2017, 10, 1720    9 of 17 

e(t) is the difference between reference power and the actual fuel cell power. 

To increase the robustness of the controller, the optimization is performed on all hourly data for 

the  entire day, which means  that  the  ITAE  index  is optimized  for  24 different operating points. 

Therefore, Equation (14) is rewritten for 24 different operating points. The objective function is given 

as, 

24 ... 2, 1, 0, = ,|).)(|.(24

0 0

ndttetJn

  (17) 

4.2. Proposed Fuzzy‐Based PI Controller Model 

The fuzzy‐based PI controller was modeled in the PSCAD environment using the SOFC‐fuzzy 

interface  system  (FIS).  Figure  6  shows  a  block  diagram  of  the  fuzzy‐logic‐based  PI  control.  A 

FORTRAN subroutine was written in PSCAD to interface with the MATLAB engine.   

 

Figure 6. Block diagram for fuzzy‐based proportional and integral (PI) control. 

The MATLAB‐FIS  system has one  input  (PFCref) and  two outputs  (Kp and Ti). The FIS  system 

receives PFCref as the input signal, and depending on the input signal an appropriate control parameter 

is sent back to the SOFC active power controller in the PSCAD environment. The FIS system consists 

of three important steps: (i) fuzzification; (ii) rule base mechanism; and (iii) defuzzification. As a first 

step,  a  set  of  input  data  (PFCref)  are  converted  into  a  fuzzy  set  using  a membership  function. A 

membership function is used in the fuzzification and defuzzification process where the set of non‐

fuzzy  inputs  is  mapped  to  fuzzy  sets.  For  this  work,  a  triangular  membership  function  was 

constructed for PFCref, Kp and Ti, given in Figure 7. The linguistic variables of input PFCref are denoted 

as Ref 1 to Ref 8, shown in Figure 7a. The linguistic variables of the output are indicated as Kp1 to Kp5 

for Kp in Figure 7b and Ti1 to Ti5 for Ti in Figure 7c, respectively. 

(a)

 (b)

Figure 7. Cont.

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Energies 2017, 10, 1720 10 of 17Energies 2017, 10, 1720    10 of 17 

 (c)

Figure 7. (a–c) shows the membership function for PFCref, Kp and Ti, respectively. 

A rule‐based mechanism was created to find the output variable for the given input. The fuzzy 

rule constructed for this work is shown in Table 1. The rule‐based mechanism has a simple if–then 

statement with a condition and conclusion. 

Table 1. Rules for fuzzy logic controller. 

 PFCref 

Ref 1  Ref 2  Ref 3 Ref 4 Ref 5 Ref 6 Ref 7 Ref 8 

Kp  Kp1  Kp1  Kp2  Kp2  Kp3  Kp3  Kp4  Kp5 

Ti  Ti1  Ti1  Ti2  Ti2  Ti3  Ti3  Ti4  Ti5 

With the help of the output membership function, the resulting fuzzy set is mapped to its output. 

The appropriate Kp and Ti from the FIS system is sent back to the PSCAD environment. The advantage 

of using fuzzy logic is that for any change in the PFCref, a specific value for the PI controller parameters 

is produced. The methodology proposed in this paper is the design of a fuzzy controller to generate 

appropriate  the real power PI controller control parameters considering  ITAE as  the performance 

criterion. The possible  limitation of  the proposed method  is  that  the  fuzzy  controller  solution  is 

specifically for the ITAE performance criterion. However, the fuzzy controller may provide varying 

solutions if different performance criteria, such as integral absolute error (IAE), and integral square 

error (ISE), were used. 

On the whole, a power management system for a grid‐connected hybrid system consisting of 

solar PV and SOFC is proposed considering varying loads and solar radiation. In order to operate the 

SOFC efficiently within a specific power range and to deliver the power set by the reference set point, 

a  fuzzy  logic  controller  is  also developed  to  generate  appropriate  control  parameters  for  the PI 

controller. The performance of the controllers is evaluated by the minimizing ITAE criterion for a 24 

h time period. 

5. Simulation Results 

5.1. Optimization of Control Parameters 

The objective of  the SOFC active power controller  is  to deliver a power set by  the  reference 

(PFCref), which  is  generated  from  the  power management module. The  control  parameters  of  the 

controller are evaluated using the GA and simplex method. The PSCAD program is equipped with 

the optimum run search engine module, which enables us to perform successive simulations for a 

group of parameters. The group of parameters generated by the optimization algorithm is used for 

simulation program and simultaneously evaluates the objective function given in Equation (14). The 

GA and simplex method present in the optimum run module were used for this study. A generalized 

simulation flow for the GA and simplex method is presented in Figure 8. The search is terminated 

when the stopping criterion is met, that is, when the algorithm completes the maximum number of 

iterations. 

The fuel cell reference set point (PFCref) changes at regular intervals due to changes in load and 

PV input power. The PI controller parameters are optimized for the SOFC reference set points (PFCref) 

for every hour. The final optimized values for different fuel cell reference set points are used for the 

Figure 7. (a–c) shows the membership function for PFCref, Kp and Ti, respectively.

A rule-based mechanism was created to find the output variable for the given input. The fuzzyrule constructed for this work is shown in Table 1. The rule-based mechanism has a simple if–thenstatement with a condition and conclusion.

Table 1. Rules for fuzzy logic controller.

PFCref

Ref 1 Ref 2 Ref 3 Ref 4 Ref 5 Ref 6 Ref 7 Ref 8

Kp Kp1 Kp1 Kp2 Kp2 Kp3 Kp3 Kp4 Kp5Ti Ti1 Ti1 Ti2 Ti2 Ti3 Ti3 Ti4 Ti5

With the help of the output membership function, the resulting fuzzy set is mapped to its output.The appropriate Kp and Ti from the FIS system is sent back to the PSCAD environment. The advantageof using fuzzy logic is that for any change in the PFCref, a specific value for the PI controller parametersis produced. The methodology proposed in this paper is the design of a fuzzy controller to generateappropriate the real power PI controller control parameters considering ITAE as the performancecriterion. The possible limitation of the proposed method is that the fuzzy controller solution isspecifically for the ITAE performance criterion. However, the fuzzy controller may provide varyingsolutions if different performance criteria, such as integral absolute error (IAE), and integral squareerror (ISE), were used.

On the whole, a power management system for a grid-connected hybrid system consisting ofsolar PV and SOFC is proposed considering varying loads and solar radiation. In order to operatethe SOFC efficiently within a specific power range and to deliver the power set by the reference set point,a fuzzy logic controller is also developed to generate appropriate control parameters for the PI controller.The performance of the controllers is evaluated by the minimizing ITAE criterion for a 24 h time period.

5. Simulation Results

5.1. Optimization of Control Parameters

The objective of the SOFC active power controller is to deliver a power set by the reference (PFCref),which is generated from the power management module. The control parameters of the controller areevaluated using the GA and simplex method. The PSCAD program is equipped with the optimum runsearch engine module, which enables us to perform successive simulations for a group of parameters.The group of parameters generated by the optimization algorithm is used for simulation program andsimultaneously evaluates the objective function given in Equation (14). The GA and simplex methodpresent in the optimum run module were used for this study. A generalized simulation flow for the GAand simplex method is presented in Figure 8. The search is terminated when the stopping criterion ismet, that is, when the algorithm completes the maximum number of iterations.

The fuel cell reference set point (PFCref) changes at regular intervals due to changes in load andPV input power. The PI controller parameters are optimized for the SOFC reference set points (PFCref)for every hour. The final optimized values for different fuel cell reference set points are used for the

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Energies 2017, 10, 1720 11 of 17

simulation. Therefore the optimal parameters found using the GA or simplex method for differentreference set points will be used throughout the simulation. The dynamic change in the controllerparameters for the simplex and GA optimization methods for different fuel cell set points are shown inFigures 9 and 10, respectively.

Energies 2017, 10, 1720    11 of 17 

simulation. Therefore the optimal parameters found using the GA or simplex method for different 

reference set points will be used throughout the simulation. The dynamic change in the controller 

parameters for the simplex and GA optimization methods for different fuel cell set points are shown 

in Figures 9 and 10, respectively. 

 

Figure 8. Generalized optimization flow using the optimum run module in PSCAD. 

(a)

(b)

Figure 9. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points 

using the simplex method. 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 231.8

2

2.2

2.4

2.6

2.8

3

3.2

Time in hours

Kp

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230

0.1

0.2

0.3

0.4

0.5

Time in hours

Ti

Figure 8. Generalized optimization flow using the optimum run module in PSCAD.

Energies 2017, 10, 1720    11 of 17 

simulation. Therefore the optimal parameters found using the GA or simplex method for different 

reference set points will be used throughout the simulation. The dynamic change in the controller 

parameters for the simplex and GA optimization methods for different fuel cell set points are shown 

in Figures 9 and 10, respectively. 

 

Figure 8. Generalized optimization flow using the optimum run module in PSCAD. 

(a)

(b)

Figure 9. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points 

using the simplex method. 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 231.8

2

2.2

2.4

2.6

2.8

3

3.2

Time in hours

Kp

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230

0.1

0.2

0.3

0.4

0.5

Time in hours

Ti

Figure 9. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set pointsusing the simplex method.

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Energies 2017, 10, 1720 12 of 17Energies 2017, 10, 1720    12 of 17 

(a)

(b)

Figure 10. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points 

using genetic algorithm (GA). 

The Kp and Ti generated by the FIS system is shown in Figure 11 for different values of input 

(PFCref). 

(a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time in hours

Kp

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time in hours

Ti

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.5

1

1.5

2

2.5

3

Time in hours

Kp

Figure 10. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set pointsusing genetic algorithm (GA).

The Kp and Ti generated by the FIS system is shown in Figure 11 for different values ofinput (PFCref).

Energies 2017, 10, 1720    12 of 17 

(a)

(b)

Figure 10. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points 

using genetic algorithm (GA). 

The Kp and Ti generated by the FIS system is shown in Figure 11 for different values of input 

(PFCref). 

(a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time in hours

Kp

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time in hours

Ti

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.5

1

1.5

2

2.5

3

Time in hours

Kp

Figure 11. Cont.

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Energies 2017, 10, 1720 13 of 17Energies 2017, 10, 1720    13 of 17 

(b)

Figure 11. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points 

using the fuzzy‐based PI controller. 

The  ranges of optimal  control parameters  for  the PI controller were obtained using  the GA, 

simplex method and fuzzy logic system are summarized in Table 2. 

Table 2. Optimal Kp and Ti ranges found using the GA, simplex method and fuzzy logic control. 

Method Control Parameter and Objective Function 

Kp  Ti  ITAE 

GA 0.750–4.958  0.0217–1.550  7844.99311 

Simplex  1.966–3.097  0.0087–0.5247  483.79171 

PSCAD‐MATLAB fuzzy logic control 1–3  0.013–0.047  73.3385 

In Table 2, the objective function evaluated for the fuzzy logic controller is lower than the other 

methods. This proves that that fuzzy‐logic‐based PI controller is efficient. In addition, the controller’s 

capability to dispatch SOFC power (PFC) matching its reference value (PFCref) can be seen in Figure 12. 

 

Figure 12. Comparison of SOFC power dispatch (PFC) matching the reference (PFCref) for the controllers. 

The SOFC reference set point (PFCref) is dependent on the change in load and PV generation. With 

reference to Figure 12, it can be seen that during the early morning hours when the PV power is zero, 

the  fuzzy‐based PI controller efficiently controls  its power supply  to  the  reference value  for  load 

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Ti

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PFC obtained using fuzzy based PI controlPFC obtained using optimal operation of simplexPFC obtained using optimal operation of GAPFCref

Figure 11. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set pointsusing the fuzzy-based PI controller.

The ranges of optimal control parameters for the PI controller were obtained using the GA,simplex method and fuzzy logic system are summarized in Table 2.

Table 2. Optimal Kp and Ti ranges found using the GA, simplex method and fuzzy logic control.

MethodControl Parameter and Objective Function

Kp Ti ITAE

GA 0.750–4.958 0.0217–1.550 7844.99311Simplex 1.966–3.097 0.0087–0.5247 483.79171

PSCAD-MATLAB fuzzy logic control 1–3 0.013–0.047 73.3385

In Table 2, the objective function evaluated for the fuzzy logic controller is lower than the othermethods. This proves that that fuzzy-logic-based PI controller is efficient. In addition, the controller’scapability to dispatch SOFC power (PFC) matching its reference value (PFCref) can be seen in Figure 12.

Energies 2017, 10, 1720    13 of 17 

(b)

Figure 11. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points 

using the fuzzy‐based PI controller. 

The  ranges of optimal  control parameters  for  the PI controller were obtained using  the GA, 

simplex method and fuzzy logic system are summarized in Table 2. 

Table 2. Optimal Kp and Ti ranges found using the GA, simplex method and fuzzy logic control. 

Method Control Parameter and Objective Function 

Kp  Ti  ITAE 

GA 0.750–4.958  0.0217–1.550  7844.99311 

Simplex  1.966–3.097  0.0087–0.5247  483.79171 

PSCAD‐MATLAB fuzzy logic control 1–3  0.013–0.047  73.3385 

In Table 2, the objective function evaluated for the fuzzy logic controller is lower than the other 

methods. This proves that that fuzzy‐logic‐based PI controller is efficient. In addition, the controller’s 

capability to dispatch SOFC power (PFC) matching its reference value (PFCref) can be seen in Figure 12. 

 

Figure 12. Comparison of SOFC power dispatch (PFC) matching the reference (PFCref) for the controllers. 

The SOFC reference set point (PFCref) is dependent on the change in load and PV generation. With 

reference to Figure 12, it can be seen that during the early morning hours when the PV power is zero, 

the  fuzzy‐based PI controller efficiently controls  its power supply  to  the  reference value  for  load 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.01

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PFC obtained using fuzzy based PI controlPFC obtained using optimal operation of simplexPFC obtained using optimal operation of GAPFCref

Figure 12. Comparison of SOFC power dispatch (PFC) matching the reference (PFCref) for the controllers.

The SOFC reference set point (PFCref) is dependent on the change in load and PV generation.With reference to Figure 12, it can be seen that during the early morning hours when the PV power is

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Energies 2017, 10, 1720 14 of 17

zero, the fuzzy-based PI controller efficiently controls its power supply to the reference value for loadchanges. It should also be noticed in Figure 12 that the fuel cell reference changes suddenly between6 a.m. to 7 a.m. due to the sudden increase in load demand from 40 kW to 54 kW, and during this timeperiod the PV power is absent. SOFC controllers tuned by the GA, fuzzy and simplex method werecapable of following the SOFC reference set point for the sudden load increase. Between 8 a.m. and7 p.m. the fuel cell reference is regulated to 20 kW for two reasons (i) during this period PV poweris available, and is more than sufficient to supply the varying load demand; and (ii) the fuel cell hasto operate within its specific power limit. Between 7 a.m. and 8 a.m. the PFCref is regulated to 20 kW,where the fuzzy controller follows the reference line exactly, but the controllers based on the GA andsimplex method take time to settle at the reference value. Further, the fuzzy-based PI controller ismore efficient after 7 p.m. that is, after sunset. After sunset, the load demand is taken care of bythe SOFC. The fuzzy-based PI controller efficiently dispatches power from the SOFC to its referencevalue from 7 p.m., thereafter supplying the peak load at 9 p.m. On the other hand, the simplexmethod and GA-based PI controller was found to be less efficient in following the reference value.The fuzzy-logic-based PI controller’s efficiency is tested during the absence of PV power.

Figure 12 shows that the SOFC controlled by a fuzzy-based PI controller is efficient where the fuelcell power (PFC) follows the reference (PFCref). It should be noted that in all the three controller types,the fuel cell is operating within its specific power range.

5.2. Application of Fuzzy-Based PI Controller for Power Management System

The results from the previous section confirmed that the fuzzy-based PI controller for SOFC activepower control is more efficient. Therefore, a simulation of the power management system was carriedout using the PSCAD-Matlab interface for the fuzzy-based PI controller for SOFC active power controlfor the hybrid system shown in Figure 1.

Load modeling is one of the important parts of a power system. Load varies throughout the dayand in some hours of the day the load reaches its maximum value and/or minimum value. In thiswork, a variable residential load is modeled with a maximum load demand reaching up to 100 kW.The daily load pattern of a residential area from [29] is used for this work. The load pattern is scaledup to a maximum load demand of 100 kW; see Figure 13.

The simulation results for the power management strategy are shown in Figure 14. Figure 14adescribes overall operating strategy of the hybrid system considering changes in load and solarradiation levels. The SOFC supplies power based on its reference value shown in Figure 12. Figure 14bshows the actual power generated from hybrid system which follows the reference.

Energies 2017, 10, 1720    14 of 17 

changes. It should also be noticed in Figure 12 that the fuel cell reference changes suddenly between 

6 a.m. to 7 a.m. due to the sudden increase in load demand from 40 kW to 54 kW, and during this 

time period the PV power is absent. SOFC controllers tuned by the GA, fuzzy and simplex method 

were capable of following the SOFC reference set point for the sudden load increase. Between 8 a.m. 

and 7 p.m. the fuel cell reference is regulated to 20 kW for two reasons (i) during this period PV power 

is available, and is more than sufficient to supply the varying load demand; and (ii) the fuel cell has 

to operate within its specific power limit. Between 7 a.m. and 8 a.m. the PFCref is regulated to 20 kW, 

where the fuzzy controller follows the reference line exactly, but the controllers based on the GA and 

simplex method take time to settle at the reference value. Further, the fuzzy‐based PI controller is 

more efficient after 7 p.m. that is, after sunset. After sunset, the load demand is taken care of by the 

SOFC. The  fuzzy‐based PI  controller efficiently dispatches power  from  the SOFC  to  its  reference 

value from 7 p.m., thereafter supplying the peak load at 9 p.m. On the other hand, the simplex method 

and GA‐based PI controller was found to be less efficient in following the reference value. The fuzzy‐

logic‐based PI controller’s efficiency is tested during the absence of PV power. 

Figure 12 shows that the SOFC controlled by a fuzzy‐based PI controller is efficient where the 

fuel cell power (PFC) follows the reference (PFCref). It should be noted that in all the three controller 

types, the fuel cell is operating within its specific power range. 

5.2. Application of Fuzzy‐Based PI Controller for Power Management System 

The  results  from  the previous section confirmed  that  the  fuzzy‐based PI controller  for SOFC 

active power control is more efficient. Therefore, a simulation of the power management system was 

carried out using  the PSCAD‐Matlab  interface  for  the  fuzzy‐based PI  controller  for  SOFC  active 

power control for the hybrid system shown in Figure 1. 

Load modeling is one of the important parts of a power system. Load varies throughout the day 

and in some hours of the day the load reaches its maximum value and/or minimum value. In this 

work, a variable residential load is modeled with a maximum load demand reaching up to 100 kW. 

The daily load pattern of a residential area from [29] is used for this work. The load pattern is scaled 

up to a maximum load demand of 100 kW; see Figure 13.   

The simulation results for the power management strategy are shown in Figure 14. Figure 14a 

describes  overall  operating  strategy  of  the hybrid  system  considering  changes  in  load  and  solar 

radiation levels. The SOFC supplies power based on its reference value shown in Figure 12. Figure 

14b shows the actual power generated from hybrid system which follows the reference.   

 

Figure 13. Daily load profile. 

From Figure 14a it is clear that the power from the SOFC is well managed during the presence 

and absence of PV power. When PV power is zero in the early morning hours and after sunset in the 

evening, any change in the load is supplied by the SOFC. Since PV power is available during the day, 

it supplies the required power needed by the load. During the day, the excess power generated from 

the hybrid system is injected into the grid, where the power injection into the grid is indicated in the 

0

20

40

60

80

100

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kW

Time in hours

Figure 13. Daily load profile.

From Figure 14a it is clear that the power from the SOFC is well managed during the presenceand absence of PV power. When PV power is zero in the early morning hours and after sunset inthe evening, any change in the load is supplied by the SOFC. Since PV power is available during

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Energies 2017, 10, 1720 15 of 17

the day, it supplies the required power needed by the load. During the day, the excess power generatedfrom the hybrid system is injected into the grid, where the power injection into the grid is indicatedin the negative in Figure 14a. If the availability of PV power is less, the power deficit required bythe load is taken care of by the SOFC. Here, the reference value for the SOFC is calculated as explainedin Section 3 and is generated by the power management module.

During the entire period of operation of the hybrid system, the SOFC power PFC changes based onthe reference value PFCref generated by the power management module, at the same time the PV arrayoperates at the maximum power point. In addition, the power imported from the grid is almost zero,which can be established from Figure 14a, where the grid power is zero or negative during the entireoperating time. From Figure 12 it is clear that the SOFC is operating within its operating range of20 kW to 100 kW. With reference to these results, it is clear that the operating strategy is simple andthat the fuzzy-based PI controller for SOFC active power control is more efficient.

It should also be noted that apart from the fuel cell, the proposed fuzzy based PI control can beapplied to any electronically-interfaced controllable distributed energy source, such as battery energysystems or capacitors.

Energies 2017, 10, 1720    15 of 17 

negative in Figure 14a. If the availability of PV power is less, the power deficit required by the load 

is taken care of by the SOFC. Here, the reference value for the SOFC  is calculated as explained  in 

Section 3 and is generated by the power management module. 

During the entire period of operation of the hybrid system, the SOFC power PFC changes based 

on the reference value PFCref generated by the power management module, at the same time the PV 

array operates at the maximum power point. In addition, the power imported from the grid is almost 

zero, which can be established from Figure 14a, where the grid power is zero or negative during the 

entire operating time. From Figure 12 it is clear that the SOFC is operating within its operating range 

of 20 kW to 100 kW. With reference to these results, it is clear that the operating strategy is simple 

and that the fuzzy‐based PI controller for SOFC active power control is more efficient.   

It should also be noted that apart from the fuel cell, the proposed fuzzy based PI control can be 

applied to any electronically‐interfaced controllable distributed energy source, such as battery energy 

systems or capacitors.   

 (a)

 (b)

Figure 14. Simulation results of the power management system. (a) Overall system operating strategy; 

(b) Hybrid system reference and actual value. 

6. Conclusions and Future Work 

In  this  study,  a  power management  strategy  for  a  grid‐connected  hybrid  PV‐SOFC  system 

supplying power at varying loads is presented. The optimal control parameters of the PI controller 

used  in SOFC active power control were found using the GA and simplex method. In addition, a 

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Figure 14. Simulation results of the power management system. (a) Overall system operating strategy;(b) Hybrid system reference and actual value.

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6. Conclusions and Future Work

In this study, a power management strategy for a grid-connected hybrid PV-SOFC systemsupplying power at varying loads is presented. The optimal control parameters of the PI controllerused in SOFC active power control were found using the GA and simplex method. In addition,a PSCAD-Matlab interface fuzzy-based PI controller was also designed to generate the optimal controlparameters for changing input.

A comparison between the three methods was performed where the GA and simplex methodSOFC active power controllers were found to be less efficient. The fuzzy-logic-based controllerensured that the output power from the SOFC followed the reference value accurately. Using thispower management strategy, the following objectives were achieved: (i) the SOFC always operateswithin a specific power range; and (ii) the power drawn from the grid is zero at all times. Operatingthe SOFC within its specific operating range increases the efficiency of the fuel cell and also enhancesthe performance of the system. The hybrid system can increase its generation when the load is heavyand decrease its generation when the load is light. In brief, the grid-connected hybrid system worksflexibly with this operating strategy. For further consideration, the proposed fuzzy logic will beimplemented for (i) effective real power control of a battery bank; and (ii) voltage and reactive powercontrol of controllable DGs.

Acknowledgments: This work was supported by the Ministry of Education Malaysia (HIR-MOHED000004-16001).

Author Contributions: Hazlie Moklis and Saad Mekhilef conceived and designed the experiments; ShivashankarSukumar performed the experiments; Marayati Marsadek and Agileswari Ramasamy analyzed the data;Shivashankar Sukumar wrote the paper.

Conflicts of Interest: The authors declare no conflict of interest.

References

1. Ren, P.S. Renewables 2015 Global Status Report; REN21 Secretariat: Paris, France, 2015.2. Hassmann, K. SOFC power plants, the Siemens-Westinghouse approach. Fuel Cells 2001, 1, 78–84. [CrossRef]3. Hatti, M.; Meharrar, A.; Tioursi, M. Power management strategy in the alternative energy photovoltaic/PEM

Fuel Cell hybrid system. Renew. Sustain. Energy Rev. 2011, 15, 5104–5110. [CrossRef]4. El-Shater, T.F.; Eskander, M.N.; El-Hagry, M.T. Energy flow and management of a hybrid wind/PV/fuel cell

generation system. Int. J. Sustain. Energy 2006, 25, 91–106. [CrossRef]5. Khanh, L.N.; Seo, J.J.; Kim, Y.S.; Won, D.J. Power-management strategies for a grid-connected PV-FC hybrid

system. IEEE Trans. Power Deliv. 2010, 25, 1874–1882. [CrossRef]6. Wang, C.; Nehrir, M.H. Power Management of a standalone Wind/PV/FC energy system. IEEE Trans.

Energy Convers. 2008, 23, 957–967. [CrossRef]7. Taher, S.A.; Mansouri, S. Optimal PI controller design for active power in grid-connected SOFC DG system.

Int. J. Electr. Power Energy Syst. 2014, 60, 268–274. [CrossRef]8. Anantwar, H.; Lakshmikantha, B.R.; Sundar, S. Fuzzy self tuning PI controller based inverter control for

voltage regulation in off-grid hybrid power system. Energy Procedia 2017, 117, 409–416. [CrossRef]9. Mishra, S.; Sahoo, S.; Dugar, A. Hybrid MVMO based controller for energy management in a grid connected

DC microgrid. In Proceedings of the IEEE Power, Communication and Information Technology Conference,Bhubaneswar, India, 15–17 October 2015; pp. 114–119.

10. Al-Saedi, W.; Lachowicz, S.W.; Habibi, D.; Bass, O. Power flow control in grid-connected microgrid operationusing particle swarm optimization under variable load conditions. Int. J. Electr. Power Energy Syst. 2013, 49,76–85. [CrossRef]

11. Laghari, J.A.; Mokhlis, H.; Bakar, A.; Mohamad, H. A fuzzy based load frequency control for distributionnetwork connected with mini hydro power plant. J. Intell. Fuzzy Syst. 2014, 26, 1301–1310.

12. Ozbay, E.; Gencoglu, M.T. Load frequency control for small hyrdo power plants using adaptive fuzzycontroller. In Proceedings of the IEEE International Conference on Systems Man and Cybermetrics (SMC),Istanbul, Turkey, 10–13 October 2010; pp. 1–5.

Page 17: A Fuzzy-Based PI Controller for Power Management of a Grid ...eprints.um.edu.my/19017/1/A_fuzzy-based_PI... · control static synchronous compensator (STATCOM) installed in a power

Energies 2017, 10, 1720 17 of 17

13. Mohagheghi, S.; Harley, R.G.; Venayagamoorthy, G.K. Modified Takagi-Sugeno fuzzy logic based controllersfor a static compensator in a multimachine power system. In Proceedings of the Conference Record ofthe IEEE 39th IAS Annual Meeting Industry Applications Conference, Seattle, WA, USA, 3–7 October 2004;pp. 2637–2642.

14. Kassem, A.M.; Zaid, S.A. Load parameter waveforms improvement of a stand-alone wind-based energystorage system and Takagi–Sugeno fuzzy logic algorithm. IET Renew. Power Gener. 2014, 8, 775–785.[CrossRef]

15. Luk, P.C.K.; Low, K.C.; Sayiah, A. GA-based fuzzy logic control of a solar power plant using distributedcollector fields. Renew. Energy 1999, 16, 765–768. [CrossRef]

16. Syed, F.U.; Ying, H.; Kuang, M.; Okubo, S.; Smith, M. Rule-Based Fuzzy Gain-Scheduling PI Controllerto Improve Engine Speed and Power Behavior in a Power-split Hybrid Electric Vehicle. In Proceedingsof the IEEE Annual Meeting of the North American Fuzzy Information Processing Society, Montreal, QC,Canada, 3–6 June 2006; pp. 284–289.

17. Berrazouane, S.; Mohammedi, K. Parameter optimization via cuckoo optimization algorithm of fuzzycontroller for energy management of a hybrid power system. Energy Convers. Manag. 2014, 78, 652–660.[CrossRef]

18. Letting, L.K.; Munda, J.L.; Hamam, Y. Optimization of a fuzzy logic controller for PV grid inverter controlusing S-function based PSO. Sol. Energy 2012, 86, 1689–1700. [CrossRef]

19. Yazdani, A.; Di Fazio, A.R.; Ghoddami, H.; Russo, M.; Kazerani, M.; Jatskevich, J.; Strunz, K.; Leva, S.;Martinez, J. Modeling guidelines and a benchmark for power system simulation studies of three-phasesingle-stage photovoltaic systems. IEEE Trans. Power Deliv. 2011, 26, 1247–1264. [CrossRef]

20. Rajapakse, A.D.; Muthumuni, D. Simulation tools for photovoltaic system grid integration studies.In Proceedings of the IEEE Electrical Power and Energy Conference (EPEC), Montreal, QC, Canada,22–23 October 2009; pp. 1–5.

21. Koohi-Kamali, S.; Rahim, N.A.; Mokhlis, H. Smart power management algorithm in microgrid consisting ofphotovoltaic, diesel, and battery storage plants considering variations in sunlight, temperature, and load.Energy Convers. Manag. 2014, 84, 562–582. [CrossRef]

22. Eltawil, M.A.; Zhao, Z. MPPT techniques for photovoltaic applications. Renew. Sustain. Energy Rev. 2013, 25,793–813. [CrossRef]

23. Larminie, J.; Dicks, A. Fuel Cell Systems Explained; John Wiley & Sons Ltd.: West Sussex, UK, 2003.24. Fedakar, S.; Bahceci, S.; Yalcinoz, T. Modeling and simulation of grid connected solid oxide fuel cell using

PSCAD. J. Renew. Sustain. Energy 2014, 6, 053118. [CrossRef]25. Zhu, Y.; Tomsovic, K. Development of models for analyzing the load-following performance of microturbines

and fuel cells. Electr. Power Syst. Res. 2002, 62, 1–11. [CrossRef]26. Wang, X.; Huang, B.; Chen, T. Data-driven predictive control for solid oxide fuel cells. J. Process Control

2007, 17, 103–114. [CrossRef]27. Li, Y.H.; Rajakaruna, S.; Choi, S.S. Control of a solid oxide fuel cell power plant in a grid-connected system.

IEEE Trans. Energy Convers. 2007, 22, 405–413. [CrossRef]28. Maiti, D.; Acharya, A.; Chakraborty, M.; Konar, A.; Janarthanan, R. Tuning PID and PI/λ D δ Controllers

Using the Integral Time Absolute Error Criterion. In Proceedings of the IEEE 4th International ConferenceInformation and Automation for Sustainability (ICIAFS), Colombo, Sri Lanka, 12–14 December 2008;pp. 457–462.

29. Lau, K.Y.; Yousof, M.F.M.; Arshad, S.N.M.; Anwari, M.; Yatim, A.H.M. Performance analysis of hybridphotovoltaic/diesel energy system under Malaysian conditions. Energy 2010, 35, 3245–3255. [CrossRef]

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